With due diligence, and a LOT of reading, you can probably figure out how to solve your solar array sizing problem. Unless you have a huge bank of storage batteries for the solar panels to dump electrical energy into, it is doubtful your panels will be sized with enough capacity to back up a geothermal heat pump. A 100 ton cooling system means it is capable of moving enough heat to melt 100 tons of ice per hour, and that requires about 350 kilo-watts of continuous power expenditure, no matter how the heat is moved.
For example, each living human being creates approximately the heat produced by a 100 watt light bulb. So a small congregation of fifty souls is going to require that you move 5 kilo-watts of heat while they occupy the church. That heat has to go somewhere, whether folks worshiping in church are wearing coats or not.
Our bodies have an excellent "closed loop" temperature control system that is pretty effective in dumping our body heat into the surrounding environment to maintain a constant body temperature near 98.6
ᵒF... on an average day (not too hot, not too cold) and with good health. The surrounding environment, that is, the air in the room, accepts our body heat while an air-conditioning system removes the heat we added to the air and dumps that heat outside. In the process of maintaining a constant temperature in air circulating within a room, an air-conditioner may also remove moisture from the air, condensing it as a liquid and lowering the relative humidity of the air. This process takes additional energy to convert water vapor in air to liquid water.
Additional heat always leaks into the church from the outside... through the walls, windows, roof, and through small gaps between doors and door frames, and small gaps between windows and window frames. It is probably impossible to prevent all drafts in a building, nor is that particularly desirable from a health point of view. You do need to circulate some fresh air from the outside to replace stale air on the inside of the church. There are published guidelines on how many air changes per hour are required. SInce the outside air is likely to require cooling, being warmer than the air inside the church, that is an additional heat load on the refrigeration system.
I haven't looked at the thermodynamic theory, or the math involved, with sizing refrigeration systems since taking courses in college during the 1970s. It is important to neither oversize nor undersize the system. Too much cooling capacity will mean too little time operating the compressor for good efficiency, a phenomenon called "
short cycling". Too little cooling capacity will mean the compressor will run more or less continuously and may never be able to cool the church to a desired temperature. Having a heat-pump does help increase electrical efficiency, but that is a separate issue that has nothing to do with how the cooling system is sized.
And finally, you need some way to prepare the interior temperature of the church for services using appropriate sensors and controls. You don't want to "cool down" too early because that wastes energy. But you want the church to be comfortable when the parishioners begin to arrive, and to "automagically" cut back on the cooling when the building is unoccupied.
it appears it may be too early to replace our collapsing steam system.
Are you using steam to drive an ammonia-cycle refrigeration system? How is the steam generated? Why is the system collapsing? Back in the day, when Coal was King, steam plants were THE way to heat and cool large campuses. Wright-Patterson AFB near Dayton, Ohio had a huge coal-fired steam plant and miles of insulated steam pipes covering several square miles of the base. Downtown Dayton also supplied coal-fired commercial steam to most of the buildings there. It's a wonderful way to move heat around if you can afford to generate high-pressure steam. Steam tunnels are always warm and toasty, even on the coldest winter days.